Explanation

Spring potential energy is given by U = 1/2kx².

If stretching to distance S gives 10 J, then to stretch to 2S, the energy becomes 1/2k(2S)² = 4×10 = 40 J.

So, additional work =  40−10 = 30 J.

Explanation

Using the identify 2 sin A cos A = sin 2A, so 2 sin 45° cos 45° = sin 90°.

Since sin 90° = 1, the expression equals 1.

Explanation

Change in momentum = 20 − 5 = 15 kg·m/s

Time = 3 s → Force = 15 / 3 = 5 N

Explanation

The phrase "washing my face" uses the correct possessive form "my."

The article "the" is necessary before "mirror" to make the sentence grammatically correct.

Explanation

Pair production occurs when a high-energy γ-ray photon is converted into an electron and a positron near a nucleus.

It is a quantum phenomenon that requires photon energy greater than 1.022 MeV.

Explanation

Step 1: Recall the formula for torque

Torque (τ) is related to the change in angular momentum (L) over time (t) by the formula: τ = ΔL / Δt

Step 2: Calculate the change in angular momentum

ΔL = 5L - 2L = 3L

Step 3: Calculate the torque

τ = ΔL / Δt = 3L / 3 = L

Explanation

Classroom management involves strategies and practices teachers use to maintain an organized, focused, and respectful learning environment.

It includes handling disruptions, organizing activities, and maintaining student engagement.

Explanation

"Do" works as a main verb (e.g., "I do my work") and also as a helping verb (e.g., "Do you understand?").

Its function changes based on how it is used in the sentence.

Explanation

"Very interesting" describes a noun by giving more information — this makes it an adjective phrase.

"Very" intensifies the adjective "interesting", forming a phrase that modifies nouns.

Explanation

Jet engines typically produce very high power, often in the megawatt (MW) range.

1.2 × 10⁶ watts equals 1.2 megawatts, which is appropriate for a jet engine.